Christopher mixes the letters S, E, L, E, C, T, E, and D thoroughly. Without looking, Allen draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that Allen will not select a consonant?

Question

A. three-eighths, 0.375, 37.5%
B. start fraction 3 over 5 end fraction, 0.6, 60%
C. start fraction 5 over 8 end fraction, 0.625, 62.5%
D. one-half, 0.5, 50%

Answer 1

There are 8 letters in total. To find the probability of not selecting a consonant, we first need to find how many consonants are in the group of 8 letters.

The consonants are S, L, C, T, and D. There are 5 consonants out of 8 total letters. Therefore, there are 8 - 5 = 3 vowels in the group.

The probability of not selecting a consonant is just the probability of selecting a vowel, which is 3/8.

This can be expressed as a decimal: 0.375

And as a percentage: 37.5%

Therefore, the answer is (A) three-eighths, 0.375, 37.5%.

Answer 2

Suppose you have a wallet with $5 bills, $10 bills, and $20 bills. If the probability of picking a $10 bill is start fraction 4 over 15 end fraction, and the probability of picking a $5 bill is one-third, what is the probability of picking a $20 bill?
A. Start Fraction 1 over 15 End Fraction
B. start fraction 1 over 5 end fraction
C. start fraction 4 over 15 end fraction
D. two-fifths

Answer 3

Let's start by using algebra to set up two equations based on the given probabilities. Let x be the probability of picking a $5 bill, y be the probability of picking a $10 bill, and z be the probability of picking a $20 bill.

We know that:

y = start fraction 4 over 15 end fraction

x = one-third

We also know that the sum of these probabilities must be 1:

x + y + z = 1

Substituting the known values, we get:

one-third + start fraction 4 over 15 end fraction + z = 1

Multiplying both sides by 15 to get rid of the fractions, we get:

5 + 4 + 15z = 15

Simplifying, we get:

15z = 6

z = start fraction 2 over 5 end fraction

Therefore, the probability of picking a $20 bill is 2/5, which is answer choice (D).